In Sec. REF , we solve the differential equations explicitly for the BH-condensate evolution with no accretion. The adiabatic approximation is assumed and the NLO analytic approximation of \(\omega _I\)  is used. We keep two dominant modes (\(\lbrace 0,1,1\rbrace \)  and \(\lbrace 0,2,2\rbrace \) ) and two subdominant modes (\(\lbrace 1,1,1\rbrace \)  and \(\lbrace 1,2,2\rbrace \) ). The GW emission rate of the \(\lbrace 0,1,1\rbrace \)  mode in Schwarzschild spacetime has been obtained in Ref. [1]}. We calculate the rates of the other three modes following their method. The BH initial spin and mass are \(a_{*0} = 0.99\)  and \(M_0=0.1/\mu \) , respectively, where \(\mu \)  is the mass of the scalar particle. The initial masses of all four condensate modes are set as \(10^{-3}M_0\) . In addition to the well-known attractor of the \(\lbrace 0,1,1\rbrace \)  mode, we also study the effect of the \(\lbrace 1,1,1\rbrace \)  attractor. In the \(\lbrace 1,1,1\rbrace \)  attractor, the energy and angular momentum of the \(\lbrace 1,1,1\rbrace \)  mode is mainly absorbed by the \(\lbrace 0,1,1\rbrace \)  mode. During this time, the BH evolves close to the \(\lbrace 0,1,1\rbrace \)  Regge trajectory (see Fig. REF ). To understand the role of different modes, we further study three more scenarios: with \(\lbrace 0,1,1\rbrace  + \lbrace 0,2,2\rbrace \)  modes, with \(\lbrace 0,1,1\rbrace  + \lbrace 1,1,1\rbrace \)  modes, and with only \(\lbrace 0,1,1\rbrace \)  mode. We made several observations by comparing these scenarios, which help us to get simple formulas to estimate the important mass and time scales. The differential equations are then solved with two more initial parameter sets, and these formulas work reasonably well for the new calculations too (see Tab. REF ).
